How do we find the point equidistant from (7, 3) and (13, -1) that lies on the line y = -9?

Answer:

13.24 ft

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have:

Sinα=opposite/hypotenuse

α=62°

opposite=x

hypotenuse=15 ft

2. When you substitute the values into  Sinα=opposite/hypotenuse, you obtain:

Sinα=opposite/hypotenuse

Sin(62°)=x/15

3. You must clear "x", as below:

x=(15)(Sin(62°))

x=13.24 ft

The answer is. 13.24 ft

(7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression (7²)⁵ * 7⁴

Since as per the rule of power we can add the power is base is same and also there is a rule if Power is the power of another power they will be multiplied

From the second rule

(7²)⁵ * 7⁴  = 7²ˣ⁵ * 7⁴

From the first rule of power

7²ˣ⁵ * 7⁴ = 7²ˣ⁵ ⁺ ⁴

therefore, (7²)⁵ * 7⁴ is equal to the expression 7²ˣ⁵ ⁺ ⁴.

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Therefore , the solution of the given problem of fraction comes out to be Stella makes 6 bows.

The definition of a fraction is a portion of a whole. A single object or a collection of objects might be the entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.

Here,

Given :

Take the amount of ribbon and divide by the amount needed per bow

5 1/3÷ 1/3

Change the mixed number to an improper fraction

(5*1 +1)/3 ÷1/3

6/3 ÷1/3

Copy dot flip

6/3 * 3/1

6

Stella makes 6 bows.

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Answer:

Step-by-step explanation:

The volume of a cone with a base radius of 4 cm and a height of 6 cm is equal to 33.51 cm³. This is calculated by using the formula V = (1/3)πr²h, where V is the volume, π is the constant Pi, r is the radius of the base, and h is the height of the cone. Plugging in the given numbers, we have V = (1/3)(3.14)(4²)(6) = 33.51 cm³.

The inner triangle's area is equal to x2 - 9.The larger triangle has a surface area of (9x2 - 16) square units.8x2 - 7 is the necessary polynomial in terms of x.

The following is the formula for determining a rectangle's area:

A = LW

The length is L.

The width is W.

For the inner triangle, see (A)

Size = x - 3

Height = x +3

(x-3)(x+3) is the inner triangle's area.

x2-3x+3x+9 is the inner triangle's area.

Inner triangle's area is equal to x2 - 9.

B) Regarding the bigger triangle

Size = 3x-4

Height 3x + 4

A = (3x-4)(3x+4)

A = 9x²+12x-12x-16

A = (9 x 2 – 16) square units

Consequently, the larger triangle's area is (9x2 - 16) square units.

C) We will make the difference in the areas in order to describe the size of the region inside the bigger rectangle by outside the smaller rectangle as a polynomial in terms of x:

P(x) is equal to the smaller triangle's area minus the larger triangle's area.

P(x) = (9x² - 16) - (x² - 9)

P(x) = 9x² - 16 - x² + 9

P(x) = 9x² - x² - 16 + 9

P(x) = 8x² - 7

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The answer of the given conditions is 255/3 =83, 368/16 = 23 and 2 210/65 = 34.

What are the numerator and denominator?

For example, 4/5 is a fraction, and the line separating the numbers 4 and 5 is the fraction bar. Here the number above the fraction bar is the numerator, and the one below the fraction bar is the denominator. A numerator represents the number of parts out of the whole, which is the denominator.

3 divided by 255 is equal to 3/255.

16 divided by 368 is equal to 16/368.

65 divided by 2 210 is equal to 65/2210.

Note that for 2 and 3 the numerator and denominator have been swapped and the division is not correct, it should be 368/16 = 23 and 2 210/65 = 34

Hence, the answer of the given conditions are 255/3 =83, 368/16 = 23, and 2 210/65 = 34.

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The equation solved is 1+-2/x²=-x-1 is 2x²+x³-2=0

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to solve the given initial-value problem: dy/dt -y=1, y(0)=0 is, u(t) = e^(t) - 1.

This can be solved using Laplace transform.

In order to translate a given derivative function with a real variable t into a complex function with a variable s, the Laplace transform is used. Let f(t) be supplied for t ≥ 0 and suppose that the function meets some later-explained requirements.

As we just saw, the Laplace transform turns partial differentials to regular differentials, making it one of the most crucial tools for solving ODEs and, more especially, PDEs. In general, applications in the time-domain for t ≥ 0 employ the Laplace transform.

Laplace transformation X is transformed linearly to a new, typically complex variable called s. Differential equations are transformed into only algebraic equations using this method.

Given that,

dy/dt -y=1

y' - y = 1

⇒ L(y') - L(y) = L(1) .....(i)

⇒L(yⁿ) = sⁿ Fy - sⁿ⁻¹y(0) - sⁿ⁻²-2y' (0) — ..... yⁿ⁻¹(0)

yⁿ means nth derivative and F(y) stands Laplace transformation of y so 1 becomes

⇒sF - y(0) - F = 1/c as L(tⁿ) = (sⁿ⁺¹) / (n!)

⇒ F(s - 1) = 1/s

⇒F = 1/(s(s - 1)) = 1/(s - 1) - 1/s

⇒L⁻¹(F) = L⁻¹ [1/(s - 1)] - L⁻¹ (1/s)

=> u(t) = e^(t) - 1

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In using a counterexample, Sarah used a single example to show that a statement was False. This technique is unlike a direct proof, in which evidence is used to support a series of statements to show why a statement is True. A single example is enough to prove a statement true.

A counterexample is a specific example that contradicts a general statement or claim. In mathematics, a counterexample is used to disprove a conjecture, hypothesis or theory by providing an example that does not follow the rule or pattern that is being proposed. It is a method of proof by contradiction.

Counterexamples can also be used to show that a conjecture or assumption is not universally true. They are important tools in mathematics and logic, as they allow us to test the validity of statements and identify any exceptions or limitations.

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The chance of the sample consisting of two college graduates with math majors who intend to teach high school is zero. There are only four people in the sample, so the sample must consist of all four people.

Since the sample size is fixed, it is impossible to have two out of the four people have the same trait (intending to teach high school). Furthermore, the sample size is too small to yield a meaningful result; the sample size would need to be much larger in order to accurately represent the population of college graduates with math majors. Therefore, the chance of the sample consisting of two college graduates with math majors who intend to teach high school is zero.

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No, it is not possible to construct a triangle with the sides 9.1cm ,8.3cm and 17.5cm because sum of the any two sides is not greater than the third side .

The side lengths are given as : 9.1cm ,8.3cm and 17.5cm  ;

we know that , the triangle is formed only when the sum of two sides of triangle is greater than third side .

applying this property , we get that ;

⇒ 9.1 + 8.3 = 17.4 > 17.5 ; False

⇒ 8.3 + 17.5 = 25.8 > 9.1 ; True

⇒ 9.1 + 17.5 = 26.6 > 8.3 ; True .

we can see that the sum of the sides 9.1 and 8.3 is 17.4 which is not greater than the third side (17.5) ,

Therefore , the triangle cannot be constructed .

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Using linear functions, we have that:

a) The equation for the line is: y = -500x + 5000

b) The prediction is 2250 sales with a price of $6.50.

The equation of a line is given by:

y = mx+ b

In which

Item a:

In this problem:

[tex]m = \frac{1500-2500}{7-5} = - \frac{1000}{2} = -500[/tex]

Thus:

y = -500x + b

Point (5,2500) means that when x=5, y = 2500, which we use to find b.

y = -500x + b

⇒2500 = -500* (5) +b

⇒2500 = -2500 +b

⇒b = 2500 +2500

⇒b = 5000

Thus

y = -500x + 5000

∴The equation for the line is: y = -500x + 5000

Item b:

y = -500*(6.5) + 5000

y = 2250

The prediction is 2250 sales with a price of $6.50.

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The researchers employed a scientific method known as Ethnography.

Ethnography to study the recorded data. Ethnography is a method of research that involves the systematic study of people and cultures, often through the use of participant observation and the collection of detailed field notes. In this case, the researchers used the recordings to gain an understanding of the student's daily activities and how they were affected by their environment.

The researcher also often conducts in-depth interviews, focus groups, or surveys with group members to comprehensively understand their perspectives and experiences.

Ethnography can be applied in various fields, including anthropology, sociology, education, and business. It is commonly used to study communities, organizations, and other social groups.

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Mrs Thomas' and Mr Carl's classes both have same lower ratio of A's to B's which expressed in the lowest term as 4:5 or fraction as 4/5

Ratio is used to compare values, and can be expressed as fractions.

Mrs Thomas' class have the ratio of students her students A's to B's as 16:20. And can be expressed as fraction in its lowest term as follows:

16:20 = 16/20

16:20 = 4/5

Mr Carl's class have the ratio of students her students A's to B's as 12:15. And can be expressed as fraction in its lowest term as follows:

12:15 = 12/15

12:15 = 4/5

Therefore, since the lowest form of Mrs Thomas' class and Mr Carl's class ratios of A's to B's are equal, then both class have equivalent lower ratio of A's to B's.

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As the corresponding angles are same in each of the right triangles, they are similar to each other (AAA rule).

AC² + BC² = AB² is true according to the Pythagorean theorem.

One of the earliest known theorems to ancient civilizations was the Pythagorean Theorem. Pythagoras, a Greek mathematician and philosopher, inspired the name of this famous theorem. He is credited with numerous mathematical contributions, some of which may have been the work of his students.

They were adamant that any two lengths had to be integral multiples of some unit length. There have been numerous attempts to conceal the fact that the square root of 2 is irrational. According to legend, the man who revealed the secret drowned at sea.

The Pythagorean Theorem describes triangles with a right angle. According to Pythagorean Theorem:

"The area of the square constructed on the hypotenuse of a right triangle equals the sum of the areas of the squares constructed on the remaining sides."

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0.1 is  Probability in Distribution Table X P(X).

What is Probability ?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

                             Statistics describes the examination of events subject to probability.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:

sum of given probabilities =(0.2+0.4+0.3) = 0.9

required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1

hence the complete probability table is

X P(X)

20 0.2

49 0.4

53 0.1

80 0.3

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The sampling distribution's mean will be interpreted as meaning A. The mean of all potential sample proportions for all samples of size 20 is equal to 0.11.

The sample proportion's sampling distribution is roughly regularly distributed. It is merely the population's mean drawn from the sampled population. This is the sample fraction of employees who arrive more than five minutes late, according to the sampling distribution's mean.

For samples of size 20, the mean of all potential sample proportions is equal to 0.11, which is the sampling distribution's mean for the sample proportion of workers who arrive at work more than 5 minutes late.

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Answer:

5 + 5z

Step-by-step explanation:

You just combine the like terms:

11 - 5 = 5

4z + 1z = 5z

=

5 + 5z

The artist should divide the region with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

Let the length of the region be l. Then, the area of the region = l x l = l^2

To divide the region into 3 equal areas, let the 3 divisions be at x1, x2, and x3 such that x1 < x2 < x3.

Then, the area of each division = (x2-x1) x l = l x (x2-x1) = l^2/3

Therefore,

l x (x2-x1) = l^2/3

or, x2 - x1 = l/3

Using this equation, we can find the values of x1, x2, and x3 that divide the region into 3 equal areas:

x1 = 0, x2 = l/3 and x3 = 2l/3

Therefore, for the given region, the artist should divide it with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

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So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

We know that the cruise ship has 2,400 regular passengers, and that 120 of them are children and 23 are teenagers. To find the fractional part of the regular passengers that are adults, we need to subtract the number of children and teenagers from the total number of regular passengers.

First, add the number of children and teenagers: 120 + 23 = 143

Then, subtract this number from the total number of regular passengers: 2,400 - 143 = 2,257

This is the number of adult passengers. To find the fraction of adult passengers, divide the number of adult passengers by the total number of regular passengers and convert the result to a fraction.

2,257/2,400 = 0.9404

So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

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Answer:

We can solve the simultaneous equations by using substitution or elimination method. Here, we will use the substitution method:

x - 2y = 3 and x ^ 2 - y ^ 2 + 2x = 10

Solving the first equation for x, we get

x = 2y + 3

Now, substitute this value of x in the second equation

(2y + 3)^2 - y^2 + 2(2y + 3) = 10

Expanding the square on the left-hand side

4y^2 + 12y + 9 - y^2 + 4y + 6 = 10

Combining like terms

3y^2 + 16y + 3 = 0

Now, we can solve this equation by factoring or using the quadratic formula. Here, we will use factoring method:

3y^2 + 16y + 3 = 0

(3y + 3)(y + 1) = 0

So, y = -1 or y = -1

Now, we can substitute either value of y back into x = 2y + 3

For y = -1, x = 2(-1) + 3 = 1

For y = -1, x = 2(-1) + 3 = 1

So, the solutions of the simultaneous equations are x = 1 and y = -1 or x = 1 and y = -1

Answer:

If y = -5, x = -7

If y = -3, x = 2 1/3 or 7/3

Step-by-step explanation:

Alr alr,

x - 2y = 3

x = 2y + 3

Now, lets substitute that into the other equation,

x² - y² + 2x = 10

(2y + 3)² - y² + 2(2y+ 3) - 10 = 0

4y² + 9 + 12y - y² + 4y + 6 - 10 = 0

3y² + 16y + 5 = 0

3y² + 15y + y + 5 = 0

3y(y + 5) + y + 5 = 0

(3y + 1)(y + 5) = 0

y = -5, -1/3

Put both these values in the first equation, u will get,

x = 2y + 3

x = -10 + 3

x = -7

or

x = -2/3 + 3

x = 2 1/3

sorry for taking this long,

My internet gave out after I was about to add the answer.

pls mark as brainliest nevertheless. I don't know why i need it, but i need it. cheers

Answer:

x > 11/-8

Step-by-step explanation:

1/5(x + 2) -1/4(2-x)> 1/3(x + 4) -1/4(5-x)

=60×1/5(x +2)-60×1/4(2-x)>60×1/3 (x+4)-60×1/4(5-x)

=12(x +2)-15(2- x)> 20(x+4)-15(5-x)

=12x + 24 - 30 + 15x > 20x + 80 - 75 + 15x

=12x + 15x - 20x -15x > 80 -75 -24 +30

=27x -35x > 80 - 99 + 30

=-8x > 11

=-8x/-8 > 11/-8

=x > 11/-8.

Hence the truth set of the inequality is said that (x : x > 11/-8).

So, on solving the provided question we can say that in the function we have m = 500, after 500 miles of driving, the expenses of the 2 plans are equal.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

f(m) = .2m + 75

f(m) = .35m

.2m + 75 = ,35m

.15m = 75

m = 500

After 500 miles of driving, the expenses of the 2 plans are equal.

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Jack's working is incorrect. To correctly find the product of 25 x 14.2 without a calculator, he should have used the distributive property of multiplication.

First, he should have broken down 25 into 20 and 5, which are easier numbers to multiply mentally. Then, he should have multiplied 14.2 by 20 to get 284, and 14.2 by 5 to get 71.

Finally, he should have added these two intermediate results, 284 and 71, to get the final answer of 25 x 14.2 = 355.

A correct working would be:

20 x 14.2 = 284

5 x 14.2 = 71

25 x 14.2 = 284 + 71 = 355

Therefore, Jack's final answer is incorrect, the correct answer is 355.

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Answer: For the first geometric sequence, the missing value is:

1 = -3/2, -2 = 7

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 1, r = -3/2, n = 3

Plugging these values into the formula:

an = ar^(n-1)

an = 1 * (-3/2)^(3-1) = 1 * (-3/2)^2 = 1 * 9/4 = 9/4

So the missing value is 9/4.

For the second geometric sequence, the missing value is:

2 = 6, 7 = 192

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 2, r = 7/6, n = 11

Plugging these values into the formula:

an = ar^(n-1)

an = 2 * (7/6)^(11-1) = 2 * (7/6)^10 = 2 * (7/6)^10 = 2 * 7^10 / 6^10 = 9261

So the missing value is 9261.

Step-by-step explanation:

11423 be the number of dogs are at the rescue center.

An expression is combination of variables, numbers and operators.

A pet rescue center is creating a monthly food budget.

The center currently has two-thirds as many dogs as cats.

Each animal is fed 2 cans of food a day.

Dog food costs $0.08 per can, cat food costs $0.05  per can

The rescue center has budgeted a total  2581.8 of  for food for this .

2(0.08)x+2(0.05)y= 2581.8

Let x be the number of dogs.

cats be y.

2/3x =y

2(0.08)x+2(0.05)2/3x= 2581.8

0.16x+0.066x=2581.8

0.226x=2581.8

x=11423

Hence, 11423 be the number of dogs are at the rescue center.

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Answer:

To find the values of x that make fg(x) > 0, we first need to find fg(x). We can do this by composing the functions, which means replacing x in g(x) with the expression for f(x):

fg(x) = f(g(x)) = f(2x + 1) = (2x + 1)^2 - 4

Now we can solve the inequality fg(x) > 0:

(2x + 1)^2 - 4 > 0

(2x + 1)^2 > 4

2x + 1 > 2 or 2x + 1 < -2

x > -1.5 or x < -2.5

So the values of x that make fg(x) > 0 are x > -1.5 or x < -2.5.

The coordinates of the new point after applying the given set of transformation is given by the ordered pair (0, -1).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:

(x, y)                                    →              (y, x)

Ordered pair A = (-4, -2)    →        Ordered pair A' = (-2, -4).

Next, we would apply a translation of 2 units to the right and 3 units up:

(x, y)                                    →              (x + 2, x + 3)

Ordered pair A' = (-2, -4)  →    (-2 + 2, -4 + 3)   →  Ordered pair A' = (0, -1).

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